Frequency selective circuits



Jan. 5 1926 l,568 ;1'44

H. w. ELSASSER FREQUENCY SELECTIVE G IR CUI'I'S Filed August 18, 1920 3 Sheets-Sheet l [meme Melyafr'ue lbaifioe 5 ATTOIiNEY f T v a,

Jan. 5 1926. 1,568,144

H. W. ELSASSER FREQUENCY SELECTIVE CIRCUITS Filed August 3, 1920 v s Sheets-Sheet 2 ATTORNEY 4 Jan. 5,1926. 1,568,144

' H. W. ELSASSER FREQUENCY SELECTIVE CIRCUITS v Filed August 13, 1920 3 Sheets-Sheet 3 INVENTOR 1% W 157mm?!- fyif flc ATTORNEY Patented Jan. 5, 1926.

UNITED STATES PATENT OFFlCE.

HENRY w. EL8AS8EE,OI NEW YORK, N. Y., ASSIG-NOB '10 AMERICAN TELEPHONE AND TELEGRAPH COMPANY, A. CORPORATION OF NEW YORK.

FREQUENCY SELECTIVE CIRCUITS.

- Application filed August 18, 1920. Serial Io. 400,870.

perio of parallel resonance, so that its imedance for a certain frequency of current 16 is very low and for another, veryhigh.

The invention proposes, further, the use of a network of'thischaracter in combination with other impedance elements in 'a periodic structure of the type illustrated and 20 described in thepatents to G, A. Campbell, 7 1,227,113 and 1,227,114 of May 22, 1917. Certain new and ,useful types of wave filters are thus arrived at, the characteristics 10f which are explained hereinbelow.

.26 This application is related to certain copending cases Serial Numbers. 403,367, 403,368, 403,369, filed of even date herewith. A good understanding of the igivention may now be'had from the following description of certain specific embodiments thereof, having reference to theaccompanying drawing, in which,

1 one orm of network embodying the inven 36' tion;

Figs. 2 to 5 inclusive are dia ifirammatic views showing various types of 'ter's"'c'om-' prising the network of F1g. 1;

Fig.1 'is w' graph showing the variation 40 with frequency in, the impedance oflthe' network of Fig. 1, and

Fi s. 2 to 5 inclusive, are graphs showing 1: e variation in attenuation of the filters of Figs. 2 to 5, respectively,

Similar characters of, reference designate similar parts in each of the several views.

The network of Fi 1 consists of an inductance L, in paralle with a path com rising an inductance'L and a condenser in series with each other. The im edance of the inductance L, is j'wL where 7 is written for the 1 1 and w. equals 20: f being the Selective Cir-.

re 1 1s a diagrammatic view showing frequency of the current. The impedance of the seriesresonant path is 1 5 I v p ,7 Hence, the impedance Z of the entire network is a 60 a L.[1 L.+,,-} ,z= ,1 (1') .7'wL1 +[7wL,+ I Place for convenience I f1=flfr where f, is the frequency at which L and C are in resonance with each other. Substitute equation 2 in equation 1 and simplifyg Then Y t (T n 15 Where I wr=2Tf I The expression within the brackets in the above equation may be placed equal to K. Then ==iw= =K where i f as I K'- The variation in the value of K with frequency is shown by theicurves' in Fig. 1", in which the values of K are ordinates and" the ratios of f to f, are abscissae. These curves indicate also the manner in which the impedance of the network changes with frequency, as may be seen by an ins ection of equation 4. At low frequencies, t e impedance of the network is a small positive value which increases as the frequency is raised until at the oint' of arallel resonance of the two at s, the vs. no thereof is 100 infinite. In passing through the resonant point the impedance changes sign and thereafter decreases with rise 1n frequency until atthe point of series resonance of the network it becomes zero. The impedance then increases until its value is again infinite at infinite frequency. It is thus seen that the network of Fig. 1 has two periods of resonance, a period of parallel resonance at one frequency and a period of series resonance at a higher frequency. The point of series resonance is dependent upon the relative values of only two of the impedance elements, namely L and C and the point of parallel resonance is governed by the relative proportions of all three of the impedance elements. The curves of Fig. 1 are drawn for an ideal network containing no resistance or other dissipative element, but in any actual case the resistance may be made so small that its effect is practically negligible. It thus appears that the network of Fig. 1 may be used as a selective networkfor passing current of series resonant frequency and preventing the passage of current of parallel resonant frequency.

I have found, moreover, that by employing the network as a shunt or series impedance in a periodic structure like that disclosed in the Campbell patents hereinbefore mentioned, certain new types of wave filters are arrived at, which filters have certain new and valuable characteristics which 1 shall now describe.

Figs. 2, 3, l and 5 illustrate four types of.

filters, employing the network of Fig. 1, the former two of these views showing the network as a shunt impedance element and the latter two, as the series impedance element of the filter section. Figs. 2 and 3 show an inductive and a capacity reactance, respectively, as the series impedance element, and Figs. 4 and 5 show the same reactances, respectively, as the shunt impedance element.

The properties of the above filters may be determined from certain mathematical exressions which set forth the relations existmg between the frequency of current and the impedance elements of the filters. In the Campbell patents hereinbefore mentioned, it was shown (equation 2) that for a periodic structure of the type now under consideration, in which the series impedance per section is Z and the shunt impedance per section is Z the attenuation per section of the filter may be derived from the relation in which denotes a propagation constant of the structure. The variation of the attenuation of any filter with frequency of current may, therefore, be deduced from equation 6, when the corresponding values of Z and Z are substituted therein. For the filter shown in Fig. 2, the value of Z is Z =jwL (7) and (according to equation 4 above),

Z =jw L K (8) The resultant equation for cosh is therefore,

Fig. 2 is a graph showing the variation of the attenuation of the filter of Fig. 2 as computed from equation 9. The axis of the abscissa: is laid off in ratios of f to f, and the axis of the ordinates in values of the attenuation constant per filter section. An inspection of the curves shows that the attenuation is nil for a range of frequencies extending between f and f At a frequency f in the upper attenuated range, the attenuation is infinite and when this frequency is chosen close to f as shown in Fig. 2 the filter has a sharp cut-off for frequencies lying just above f The frequencies f f and f may be evaluated as follows: It was shown in the said Campbell patents that for unattenuated transmission must be a ure ima inary, and that, therefore, the value of cos must lie between *1. The frequencies which limit the ranges of free transmission may consequently be determined by placing equation 9 equal to +1 and -1 respectively and solving for f.-, WVhen this is done, it will be found that the roots are, respectively,

The frequency f at which the attenuation is infinite, may be evaluated by placing equation (9) equal to co and solving for f, whence The attenuation characteristics of the remaining filters may he arrived at in a similar manner. The curves of Fig. 3' show that the filter of Fig. 3 passes without substantial attenuation two ranges of frequencies, one of which extends between f and f and the other from f, to 00. The filter has, therefore, the combined characteristics of a highpass and a band filter, and serves the pur poses of both. It has, moreover, a frequency f at which the attenuation is infinite. This frequency may be chosen close to f thus giving the filter a sharp cut-off forlfrcquencies just below the high pass range.

The frequencies f f f and f may be evaluated similarly as the limiting frequencies of the filter of Fig. 2. The expression for cosh in the present case is, since 0.

is a capacity reactance,

Placing equation- 13 equal, res ctively, to +1 and -1 and solving for f, t e roots will be found to. be

f4 When equation 14 is placed equal to 1m and solved for. f, the frequency of maximum attenuation is found to be i 1 fm=m (17).

The curves of Fig. 4* show that the filter of Fig. 4 is similar tothat of Fig. 2 in that it has a single band of free transmission. It differs therefrom, however, in that the frequency f,,,, at which the attenuation is infinite, lies in the lower attenuated range, thus giving this filter a sharp cutoff for frequencies lyin below f These curves have been erived from the expression a P5 cosh/ A +1 (18) which is similar to e nation 9 above except that the values of k, and Z are interchanged, the shunt impedance of Fig. 2 belng the series impedance of Fig. 4, and vice versa. The "limiting frequencies are obtained, as before, by placing cosh equal to +1 and 1 respectively, and solving for and q 1 fh 2 \/Ea 20 The expression for the frequency of maximum attenuation, 'f is-obtained by lacing cosh equal to co and solving or f. Then and the values of f,, f,, f,, f, and f are It should be noted that the attenuation curves illustrated herein refer to the ideal structure in which the resistance of the impedance units is zero. In a practical filter .here is a departure from these curves, owing to energy dissipation. In any case, however, the resistance may be made so small that the departure from the ideal is practically negligible.

The formulae 10-12, 1417, 19-21, and 23-26, given above, may be used in designing filters tomeet any specified sets of conditions. Since there are four independent impedance elements in each filter section, any four properties of the filter dependent upon the values of the impedance elements but independent of each other may be chosen at will. For example, in the design of a filter of the type illustrated in Fig. 8, two of the design conditions may be taken as the frequencies f and f and a third as i thus defining the ranges of free transmission. This leaves one condition open to choice, and this may be taken as the impedance of the filter at any desired frequency, or as the value of any one of the elements of the filter section. In the design of a filter of the type of Fig. 2, two of the design conditions may be chosen as the frequencies f and f and the third as f,,,, thus leaving the fourth to be chosen in accordance with any other condition that may prevail. Similar considerations apply to the remaining types of filters.

As an example of the application of the formulae, let it be required to design a filter of the type illustrated in Fig. 3, which shall transmit frequencies between 400 and 2500 cycles and which shall pass also all frequencies of 5,000 cycles or higher. Frequencies f f and f, are thus specified as 4.00, 2500, and 5,000 cycles respectively. As a fourth design, factor, let it be assumed that certain considerations dictate that the value of C shall be .1 microfarad. This leaves three of the constants of the filter section, namely L L and C to be evaluated. Equations 14, 15, and 16 are three simultaneous equations involving the three unknowns, as well as the quantities f f f, and C the values of which have been assumed. These equations may therefore be solved when the assumed quantities are'substituted therein, and when this is done it will be found that L,:.388 henries L :.133 henries (1 2.0077 8 microfarads All the constants of the filter are thus determined. It will readily be seen that, in-

stead of the above-mentioned set of conditions, any others involving the filter impedances may be imposed, it being understood that the above example is merely a simple -illustration, and in no way limits the invention.

Although only certain forms-of filters embodying the invention are shown and described herein, it is readily understood that various changes and modifications may be made therein within the scope of the following claims, without departing from the spirit and scope of the invention.

What is claimed is:

1. A wave filter of the type having similar recurrent sections, each section comprising a series element and a shunt element, and one of those elements consisting of a single lumped reactance, the other element being a network comprising an inductive reactance in parallel with a path comprising an inductive reactance and a capacity reactance in series with each other.

2. A filter for an electric circuit, consisting of a plurality of recurrent sections, each section comprising an impedance in series with the circuit and an impedance in shunt thereto, one of said impedances consisting of a single reactance element and the other of a network comprising an inductive reactance in parallel with a path comprising a capacity reactance in series with an inductive reactance. I

.3. A wave filter of the type having recurrent sections, each section comprising a series .impedance and a shunt impedance, one of 9 these two impedances being a.network of three reactances, and the other impedance being a coil whereby the filter is given a single transmission range between finite limiting frequencies and infinite attenuation at a point outside that transmission range.

4. The method of discriminating among various alternating current components according to their frequency, which consists in attenuating those components from zeroto a certain finite frequency, then passing the components from that finite frequency to a certain higher finite frequency, and then attenuating all components above said last mentioned limiting frequency with a maximum of attenuation at a frequency a little greater than said last mentioned limiting frequency.

In testimony whereof, I have signed my name to this specification this 10th day of August 1920.

HENRY w. ELSAS-SER. 

